Let $E$ be an eliptic curve over a finite field $\Bbb F_q$ of order $q$.
Let $m$ be an integer relatively prime to $q$.
Why is $E[n](\overline{\Bbb F}_q)\cong\Bbb Z_n\times\Bbb Z_n$?
It's obvious from Lagrange theorem that it is divisible by $\Bbb Z_n$, but why is the number of left cosets also $n$?